If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?

Question

Mathematics

Vivian Myers

Today, 03:51

If sin Θ = negative square root 3 over 2 and π < Θ < 3 pi over 2, what are the values of cos Θ and tan Θ?

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Romero · Answer 1

Sin (teta) = - √3/2

pi
because of range of pi we can conclude that teta is in third quadrant of x-y coordinate system which will determine us what is the sign of cos (teta) and tan (teta)

cos (teta) = √ (1-sin^2 (teta)) = 1/2

but because teta is in third quadrant, cos (teta) has to be negative which means:

cos (teta) = - 1/2

tan (teta) = sin (teta) / cos (teta) = √3

tan of an angle that is in third quadrant is positive which is what we got.

Answer is:

cos (teta) = - 1/2

tan (teta) = √3